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x^(3)-81 x

x3−81x x^{3}-81 x

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Multiply powers: integer basesright chevron icon

Full solution

Q. x3−81x x^{3}-81 x
  1. Identify Common Factor: Identify the common factor in both terms of the expression x3−81xx^3 - 81x. Both terms have an xx in common, so we can factor out an xx.
  2. Factor Out 'x': Factor out the common x from the expression.\newlinex3−81xx^3 - 81x can be factored as x(x2−81)x(x^2 - 81).
  3. Recognize Difference of Squares: Recognize that the expression inside the parentheses is a difference of squares. x2−81x^2 - 81 can be factored further because it is a difference of squares (a2−b2)(a^2 - b^2), where a=xa = x and b=9b = 9.
  4. Factor Difference of Squares: Factor the difference of squares. x2−81x^2 - 81 factors into (x+9)(x−9)(x + 9)(x - 9).
  5. Write Fully Factored Form: Write the fully factored form of the original expression.\newlineThe factored form of x3−81xx^3 - 81x is x(x+9)(x−9)x(x + 9)(x - 9).

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